# How does one use NSum within NIntegrate properly?

If I use symbolic integration for the following:

Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}]


336

as one can see it gives the answer as it seems to 'understand' the sum integral.

However with

NSum[NIntegrate[i + x, {x, 1, 7}], {i, 1, 7}]


NIntegrate::inumr: The integrand i+x has evaluated to non-numerical values for all sampling points in the region with boundaries {{1,7}}.

336.

As one can see it does not seem to know that $$i$$ is 1 I think or something like that.

What is the problem and how can I format the numerical functions to do what I want without these errors?

• FWIW: Sum[NIntegrate[...]] works just fine. – AccidentalFourierTransform Jun 24 '19 at 13:28
• Use Quiet[] or ignore it. NSum[] is evaluating its argument symbolically probably to see if it can be differentiated – Michael E2 Jun 24 '19 at 22:09

Define a function that can only be called with a numerical argument $$i$$:
f[i_?NumericQ] := NIntegrate[i + x, {x, 1, 7}]

NSum[f[i], {i, 1, 7}]